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A Problem Text in Advanced Calculus by John M. Erdman
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About this book :- The proofs of most of the major results are either exercises or problems. The distinction here is that solutions to exercises are written out in a separate chapter in the ProblemText while solutions to problems are not given. This arrangement will provide flexibility for instructors who wish to use it as a text. For this text to be useful a student should have previously studied introductory calculus, more for mathematical maturity than anything else. Familiarity with properties of elementary functions and techniques of differentiation and integration may be assumed and made use of in examples—but is never relied upon in the logical development of the material.
Book Detail :- This book has following details information. Title: A Problem Text in Advanced Calculus by John M. Erdman Publisher: Portland State University Year: 2008 Pages: 377 Type: PDF Language: English ISBN-10 #: 1470442469 ISBN-13 #: 978-1470442460 License: CC Get this book from Amazon
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Book Contents :- This book has following table of contents. Intervals - Topology of the Real Line - Continuous Functions from R to R - Sequences of Real Numbers - Connectedness and the Intermediate Value Theorem - Compactness and the Extreme Value Theorem - Limits of Real valued Functions - Differentiation of Real Valued Functions - Matric Spaces - Interiors, Closures and Boundaries - The Topology of Metric Spaces - Sequences in Matric Spaces - Uniform Convergence - More on Continuity and Limits - Compact Metric Spaces - Sequential Characterization of Compactness - Connectedness - Complete Spaces - Applications of a Fixed Point Theorem - Vector Spaces - Linearity - Norms - Continuity and Linearity - The Cauchy Integral - Differential Calculus - Partial Derivatives and Iterated Integrals - Computations - Infinite Series - The Implicit Function Theorem
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